It depend on if you upgraded your equipment or still use the equip of an apprentice. High experience in crafting something can't do much if the equip is shit.
If you can't get it near 100% then the equip is not good enough (or you messed up your skills)
Your example with rolling a d20 to open a door will be 100% with a nomal hand (good equip), 75% with a broken hand and 25% if the whole arm is broken. And 0% if you are armless
